A Butler-type oscillation theorem for second-order dynamic equations on discrete timescales

Abstract

In this paper, we consider an extension of some results to dynamic equations on discrete timescales originally due to Butler for second-order superlinear differential equations. As an application, we get that the superlinear difference equation

is oscillatory, if .

Keywords::

• superlinear
• dynamic equation
• timescale
• non-oscillatory solution

2000 Ams Classification number::

• 34K11
• 39A10
• 39A99

Acknowledgements

The authors would like to thank the referees for their detailed comments on an earlier version of this paper.

Notes

^1. B. Jia was supported by the National Natural Science Foundation of China (Nos 10971232 and 11271380) and Guangdong Province Key Laboratory of Computational Science. Email: [email protected]

^2. Email: [email protected]